Stochastic volatility models on option pricing have received much study following the discovery of the non-at implied surface following the crash of the stock markets in 1987. The most widely used stochastic volatility model is introduced by Heston (1993) because of its ability to generate volatility satisfying the market observations, being non-negative and mean-reverting, and also providing a closed-form solution for the European options. However, little research has been done on Heston model used to price early-exercise options. This presumably is largely due to the absence of a closed-form solution and the increase in computational requirement that complicates the required calibration exercise. This thesis examines the performance of the Heston model versus the Black-Scholes model for the American Style equity option of Microsoft and the index option of S&P 100 index. We employ a finite difference method combined with a Projected Successive Over-relaxation method for pricing an American put option under the Black-Scholes model, while an Alternating Direction Implicit method is utilized to decompose a multi-dimensional partial differential equation into several one dimensional steps under the Heston model. For the calibration of the Heston model, we apply a two step procedure where in the first step we apply an indirect inference method to historical stock prices to estimate diffusion parameters under a probability measure and then use a least squares method to estimate the instantaneous volatility and the market risk premium which are used to switch from working under the probability measure to working under the risk-neutral measure. We find that option price is positively related with the value of the mean reverting speed and the long-term variance. It is not sensitive to the market price of risk and it is negatively related with the risk free rate and the volatility of volatility. By comparing the European put option and the American put option under the Heston model, we observe that their implied volatility generally follow similar patterns. However, there are still some interesting observations that can be made from the comparison of the two put options. First, for the out-of-the-money category, the American and European options have rather comparable implied volatilities with the American options' implied volatility being slightly bigger than the European options. While for the in-the-money category, the implied volatility of the European options is notably higher than the American options and its value exceeds the implied volatility of the American options. We also assess the performance of the Heston model by comparing its result with the result from the Black-Scholes model. We observe that overall the Heston model performs better than the Black-Scholes model. In particular, the Heston model has tendency of underpricing the in-the-money option and overpricing the out-of-the-money option. Whereas, the Black-Scholes model is inclined to underprice both the in-the-money option and the out-of-the-money option.b

Large amounts of hydrocarbon reserves are trapped in fractured reservoirs where fluid flux is far more rapid along fractures than through the porous matrix, even though the volume of the pore space may be a hundred times greater than the volume of the fractures. These are considered extremely challenging in terms of accurate recovery prediction because of their complexity and heterogeneity. Conventional reservoir simulators are generally not suited to naturally fractured reservoirs’ production history simulation, especially when production processes are associated with large pressure and temperature changes that lead to large redistribution of effective stresses, causing natural fracture aperture alterations. In this case, all the effective processes, i.e. hydraulic, thermal and geomechanical, should be considered simultaneously to explain and evaluate the behavior of stress-sensitive reservoirs over the production period. This is called thermo-hydro-mechanical (THM) coupling. In this study, a fully coupled thermo-hydro-mechanical approach is developed to simulate the physical behavior of fractures in a plane strain thermo-poroelastic medium. A hybrid numerical method, which implements both the finite difference method (FDM) and the displacement discontinuity method (DDM), is established to study the pressure, temperature, deformation and stress variations of fractures and surrounding rocks during production processes. This method is straightforward and can be implemented in conventional reservoir simulators to update fracture conductivity as it uses the same grid block as the reservoir grids and requires only discretization of fractures. The hybrid model is then verified with couple of analytical solutions for the fracture aperture variation under different conditions. This model is implemented for some examples to present the behavior of fracture network as well as its surrounding rock under thermal injection and production. The results of this work clearly show the importance of rate, aspect ratio (i.e. geometry) and the coupling effects among fracture flow rate and aperture changes arising from coupled stress, pressure and temperature changes. The outcomes of this approach can be used to study the behavior of hydraulic injection for induced fracturing and promoting of shearing such as hydraulic fracturing of shale gas or shale oil reservoirs as well as massive waste disposal in the porous carbonate rocks. Furthermore, implementation of this technique should be able to lead to a better understanding of induced seismicity in injection projects of all kinds, whether it is for waste water disposal, or for the extraction of geothermal energy.

MODELING AND NUMERICAL ANALYSIS OF SINGLE DROPLET DRYING DALMAZ, Nesip M.Sc., Department of Chemical Engineering Supervisor: Prof. Dr. H. &Ouml / nder &Ouml / ZBELGE Co-Supervisor: Asst. Prof. Dr. Yusuf ULUDAg August 2005, 120 pages A new single droplet drying model is developed that can be used as a part of computational modeling of a typical spray drier. It is aimed to describe the drying behavior of a single droplet both in constant and falling rate periods using receding evaporation front approach coupled with the utilization of heat and mass transfer equations. A special attention is addressed to develop two different numerical solution methods, namely the Variable Grid Network (VGN) algorithm for constant rate period and the Variable Time Step (VTS) algorithm for falling rate period, with the requirement of moving boundary analysis. For the assessment of the validity of the model, experimental weight and temperature histories of colloidal silica (SiO2), skimmed milk and sodium sulfate decahydrate (Na2SO4&amp / #8901 / 10H2O) droplets are compared with the model predictions. Further, proper choices of the numerical parameters are sought in order to have successful iteration loops. The model successfully estimated the weight and temperature histories of colloidal silica, dried at air temperatures of 101oC and 178oC, and skimmed milk, dried at air temperatures of 50oC and 90oC, droplets. However, the model failed to predict both the weight and the temperature histories of Na2SO4&amp / #8901 / 10H2O droplets dried at air temperatures of 90oC and 110oC. Using the vapor pressure expression of pure water, which neglects the non-idealities introduced by solid-liquid interactions, in model calculations is addressed to be the main reason of the model resulting poor estimations. However, the developed model gives the flexibility to use a proper vapor pressure expression without much effort for estimation of the drying history of droplets having highly soluble solids with strong solid-liquid interactions. Initial droplet diameters, which were calculated based on the estimations of the critical droplet weights, were predicted in the range of 1.5-2.0 mm, which are in good agreement with the experimental measurements. It is concluded that the study has resulted a new reliable drying model that can be used to predict the drying histories of different materials.

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abstract: In sub transmission systems, many more raptor deaths have been recorded near metal poles rather than wood poles. The metal pole, which is reliable in structure but also grounded, may increase the risk of electrocution when raptors perch on the insulator. This thesis focuses on evaluating the effectiveness of the raptor guard to prevent both debilitating and lethal electrocutions to local wildlife in 69 kV sub transmission systems. First, the two-dimensional (2D) finite difference methods (FDM) were proposed to solve the Poisson and Laplace equations, which describe the electric field. Second, the verification of the FDM algorithm was made based on a parallel-plate capacitor model. Then, the potential and the electric field were simulated by the raptor-insulator model to evaluate the possibility of flashover and leakage current under various conceivable scenarios. Third, several dielectric performance experiments were implemented to gain insight into the physical property of the raptor guard developed by the Salt River Project (SRP) as an example. The proposed initial-tracking-voltage and time-to-track experiments tested the ability of the guard, which is designed to prevent the tracking phenomenon under a contaminated situation such as rain, fog, and snow. A data acquisition also collected the leakage current data for the comparison of maximum raptor tolerance. Furthermore, the puncture voltage of this guard material was performed by the dielectric breakdown voltage experiment in an oil-covered container. With the combination of the model simulation and the experiments in this research, the raptor guard was proven to be practical and beneficial in sub transmission system. / Dissertation/Thesis / Masters Thesis Electrical Engineering 2016

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Orientador: Hugo Enrique Hernandez Figueroa / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação / Made available in DSpace on 2018-08-05T08:31:54Z (GMT). No. of bitstreams: 1 Ambrosio_LeonardoAndre_M.pdf: 2415252 bytes, checksum: c4357386bcd33e0676d894544a47c85e (MD5) Previous issue date: 2005 / Resumo: Este trabalho apresenta um modelo numérico baseado no método das diferenças finitas no domínio do tempo, com objetivo de analisar as características da taxa de absorção específica, SAR, na cabeça humana, mediante um modelamento quiral das equações de Maxwell. A formulação é expressa em termos dos campos polarizados elétrico e magnético, permitindo investigar possíveis variações de SAR na cabeça humana, para diferentes valores de quiralidade, através de algoritmos simples. Tais algoritmos tornam possíveis a análise das diversas características da SAR em estruturas bidimensionais, representando secções transversais da cabeça humana, discretizada em seus tecidos de volumes significativos. Uma verificação foi feita calculando se a estabilidade numérica e simulando uma fonte pontual em um meio quiral. As influências da impedância equivalente da antena e da distância entre a antena e a cabeça humana foram investigadas, para diferentes valores quirais, bem como é feita a análise da SAR local média e sua variação percentual para os valores quirais escolhidos. Cinco cortes transversais foram analisados, com o objetivo de verificar características e comportamentos globais de SAR, evitando assim que variações locais fossem assumidas como um efeito global / Abstract: This work shows a numerical model based on the finite-difference time-domain method, with the aim of analysing the characteristics of the Specific Absorption Rate, SAR, in a human-head, through a quiral modeling of Mawell¿s equations. The formulation is expressed in terms of the electric and magnetic wave-fields, allowing to investigate possible changes in SAR, inside the human head, for different values of chirality, using simple algorithms. Such algorithms, make the analysis of the several characteristics of SAR in bidimensional structures representing the transversal layers of the human head, discretized in its tissues possessing significant volumes. A verification was made by calculating the numerical punctual stability and by simulating a punctual source in a chiral medium. The influences of the equivalent impedances of the antenna and of the distance between the antenna and the human head are analysed, for different chiral values, as well as an analysis of the average local SAR and its percentual variation for chosen chiral values. Five transversal layers were analysed, with the aim of verifying global characteristics and behaviors of SAR, avoiding that local variations were assumed as a global effect / Mestrado / Telecomunicações / Mestre em Engenharia Elétrica

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Submitted by Almir Azevedo (barbio1313@gmail.com) on 2014-05-09T16:42:31Z No. of bitstreams: 0 / Made available in DSpace on 2014-05-09T16:42:31Z (GMT). No. of bitstreams: 0 Previous issue date: 2013 / Empregando a equação de difusão de nêutrons em estado estacionário multidimensional para simular o fluxo de nêutrons em reatores refrigerados água, e fazendo uso do Método de Diferenças Finitas, o presente trabalho tem por objetivo apresentar um estudo sobre o comportamento da distribuição de potência num reator tipo PWR, considerando a intensidade e a migração dos picos de potência à medida que ocorre a inserção das barras de controle no núcleo. Além disso, tomando como ponto de partida a distribuição axial de potência ao longo da vareta de maior fluxo de calor, realiza-se a análise térmica dessa vareta e do canal refrigerante associado. Para tal é empregado o código Fuel_Rod_3D, que usa o Método dos Elementos Finitos para modelar uma vareta combustível e seu canal refrigerante, possibilitando a simulação do comportamento termohidráulico de uma única vareta discretizada em três dimensões, considerando o fluxo de calor a partir do interior da pastilha combustível, passando pelo "gap" e pelo revestimento até alcançar o fluido refrigerante / This Work aims to present a study about the power distribution behavior in a PWR type reactor, considering both intensity and migration of power peaks due to insertion of control rods into the core. Employing the multidimensional steady-state neutron diffusion equation in order to simulate the neutron flux, and using the Finite Difference Method. Furthermore, based on the axial power distribution on the largest heat flux rod, is carried out thermal analysis of this rod and associated coolant channel. For this purpose is employed the Fuel_Rod_3D code, it uses the Finite Element Method to model the fuel rod and the associated coolant channel, allowing the thermohydraulics simulation of a single rod discretized in three dimensions, considering the heat flux from the pellet, crossing the gap and the cladding until it reaches the coolant.